A New Algorithm for Finding Trees with Many Leaves

  • Joachim Kneis
  • Alexander Langer
  • Peter Rossmanith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)


We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Spanning Out-Tree in the case of directed graphs. The run time of our algorithm is \(O({\it poly}(|V|) + 4^k k^2)\) on undirected graphs, and O(4 k |V| ·|E|) on directed graphs. This improves over the previously fastest algorithms for these problems with run times of \(O({\it poly}(|V|) + 6.75^k {\it poly}(k))\) and \(2^{O(k \log k)} {\it poly}(|V|)\), respectively.


Span Tree Directed Graph Undirected Graph Recursive Call Find Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Joachim Kneis
    • 1
  • Alexander Langer
    • 1
  • Peter Rossmanith
    • 1
  1. 1.Dept. of Computer ScienceRWTH Aachen UniversityGermany

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